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Properties

Label 5292.2.w
Level $5292$
Weight $2$
Character orbit 5292.w
Rep. character $\chi_{5292}(521,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $80$
Newform subspaces $3$
Sturm bound $2016$
Trace bound $13$

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Defining parameters

Level: \( N \) \(=\) \( 5292 = 2^{2} \cdot 3^{3} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 5292.w (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 63 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 3 \)
Sturm bound: \(2016\)
Trace bound: \(13\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(5292, [\chi])\).

Total New Old
Modular forms 2160 80 2080
Cusp forms 1872 80 1792
Eisenstein series 288 0 288

Trace form

\( 80 q + O(q^{10}) \) \( 80 q - 12 q^{11} + 3 q^{13} + 9 q^{17} + 33 q^{23} - 40 q^{25} + 6 q^{29} - q^{37} - 6 q^{41} + 2 q^{43} - 36 q^{47} + 12 q^{53} - 30 q^{59} - 14 q^{67} + 10 q^{79} - 12 q^{85} + 21 q^{89} + 3 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(5292, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
5292.2.w.a 5292.w 63.i $16$ $42.257$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+\beta _{15}q^{5}+(-\beta _{4}+\beta _{5})q^{11}+(\beta _{3}+\beta _{10}+\cdots)q^{13}+\cdots\)
5292.2.w.b 5292.w 63.i $16$ $42.257$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+\beta _{11}q^{5}+(-\beta _{2}+\beta _{3}-\beta _{4}+\beta _{6}+\cdots)q^{11}+\cdots\)
5292.2.w.c 5292.w 63.i $48$ $42.257$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$

Decomposition of \(S_{2}^{\mathrm{old}}(5292, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(5292, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(126, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(189, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(252, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(378, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(441, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(756, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(882, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1323, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1764, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(2646, [\chi])\)\(^{\oplus 2}\)